I find zero to be an interesting concept in the applied math world because depending on how you want to visualize it, it leads to different numerical methods.

I find zero to be an interesting concept in the applied math world because depending on how you want to visualize it, it leads to different numerical methods. For example, think of how we represent a zero vector on a computer. Basically, we have an array of floating point numbers, but it's sort of hard to exactly pin down when we want to define this array as zero. We could look at all of the individual elements; we could sum them; etc. Anyway, the two most used methods are to call a vector zero when its norm is zero or to call a vector zero when it's orthogonal to all other vectors in the space. The first approach leads to least-squares approaches, which gives things like GMRES or QMR in linear algebra or first-order system least-squares (FOSLS) finite element methods. The second approach leads to Galerkin and Petrov-Galerkin algorithms, which gives things like CG in linear algebra or more standard Galerkin or Petro-Galerkin finite element methods. Anyway, that's just an aside, but I wanted to add that how we visualize zero has a definite computational, algorithmic affect.